Other answers may well be much more detailed, of course, but hopefully this gives the gist of what I think might be a useful type of answer. Things like useful formats (JSON, XML) would be interesting to Jeff Atwood too, I'm sure.

I've got an Android version in the works but I stopped for a while to wait and see how use of the iPhone app did, wait for the other sites to be added to the dump and hold out hope for an API. It seems like things are coming together now.
– carsonJan 15 '10 at 14:01

+1 for "Something happened in a question I commented on." because there is no direct means within SO to go back to my comments.
– RichardJan 16 '10 at 11:18

@Richard: [aside from the fact that you have just been notified of this very comment reply, but that only works as of today] you can at least go back to your recent comments; they are on the activities page of your profile
– balphaJan 16 '10 at 20:16

@balpha: Indeed, but it is pretty limited. Some days on SO the activity log is not enough for the last 24hours. I have at times wanted to get back to a question or answer I recall commenting on, but am left trying to search for it (which is, at best, hit and miss).
– RichardJan 17 '10 at 10:47

I want to build a notification icon for the system tray that pops up a notice (like Outlook or Messenger) for the following events:

new questions meet certain criteria (tags + regex match)

someone adds or changes any content in a question where I've participated

votes on anything I've posted.

I thinking about how to design an API for this, what I'd really like is a type/class I can use that raises events, rather than a service I poll. Let the Stack Overflow team worry about how to poll the service by providing the class that does that part, and then they can be sure everyone is nice about it. It also takes that burden off of individual programmers, so it's easier to get started. The downside is that it limits you to supported platforms, rather than everyone (though there's nothing stopping them from exposing the base service as well).

Looking a little lower level, some things I might need to be able to do:

Get "new" questions (for some definition of new that probably involves passing in the datetime of my last check)

Either:

Get a list of question ids a user has participated in AND

Get new activity in a specific question or list of questions (by id)

OR

Get all new activity

Determine whether a user has participated in a question that holds a specific ID

New up/down votes cast on a specific user

When I say "new activity", I mean which question ID changed, which post ID (if any) within the question changed, a summary of the change (new post, deleted post, edited x characters, closed, etc), and who did it.

Additionally, if you ever want to support updating via the API, you probably want to include OpenID authentication in this version as well.

I would like to replace the current API I use for my Stack Overflow iPhone application that currently uses the Creative Commons (CC) dump. Since the bundling of the dumps changes every month I end up having to update my API by hand so I would really like to see an API not to mention having access to the data faster.

The DesiredSOApi document is pretty close to what I would need now and would allow me to add a lot more functionality but I do see some missing parts:

A way of communicating errors needs to be described in the document. I assume it would be via HTTP response codes.

It would be better if the specific question call optionally included all answers and comments that went with the question. The question ID and title would also be nice to include.

I think that it would be easier to handle HTTP being returned from those parts that would return HTTP than Markdown. I think I remember a podcast where it was said that HTML is stored in the database so this may be a non-issue. However, if Markdown is available, it would also be nice to have a way to get HTML too.

This may be more of a stretch but it would be nice to register for updates to be pushed as opposed to requiring a poll for them. I would imagine that the Stack Overflow TweetDeck idea would benefit from this as well. I currently have an unexposed feature in the iPhone app that would let users watch questions to get push notifications on changes and it makes me cringe to think about polling for that.

A more radical and probably simpler approach to this could be to create a "firehose" of all the acceptable data coming out of Stack Overflow and then let everyone do what they will with it. Much like getting the CC dump but in realtime.

Would pubsubhubbub help on the notification front?
– Jon SkeetJan 15 '10 at 14:08

The data format seems to be stabilizing... there are still small changes, but give it a few more things and I think it will settle down.
– Joel CoehoornJan 15 '10 at 14:16

@Jon That was what I was thinking but I'm not sure if there is wide acceptance of it yet. SO could be a good place to get people on board.
– carsonJan 15 '10 at 14:51

@Joel Lately the biggest issue for me is the directory structure changes with each new dump. I am so close to being able to automate it all. It won't matter once this API is ready. :)
– carsonJan 15 '10 at 14:55

I also mentioned the "firehose" request on the SO blog (before I saw this question).
– Greg HewgillJan 16 '10 at 1:41

I would love to see the iPhone app extended for all three trilogy sites
– Mark HendersonJan 17 '10 at 3:50

You make a good point about error conditions. HTTP responses are the obvious and now document solution. Markdown is more descriptive than the HTML equivalent (and going from HTML -> Markdown is basically unsupported) so I think returning markdown is really the best bet. Plus SO's Markdown implementation is now open source.
– Kevin Montrose♦Jan 17 '10 at 4:14

I want to create visualisations that depict and map the relationships between technologies based on developer exposure to said technologies and tags. To do this, I need to be able to discover tags for questions that a user has asked or answered.

A bridge to the netherworld... dare I say it, the forbidden taboo F-word... Facebook.

Phase 1. Announce questions asked, badges earned, and best answers. Would be ideal if this the API can be configured to pingback a URL for requested users, so that this information can effectively be pushed to Facebook.

I want to get a particular user's activity both recent and in the past. [I have to use Activity page because a lot of time Eric leaves interesting comment but no answer. And there is no way to look at all comments done by a user.]

E.g. I follow activity pages for Eric, Pavel and Jon. I have to do this daily otherwise I would miss their comments/answers if it scrolls off the activity page. I could potentially build a website which lets me view a particular user's activity in any way I choose. [E.g. filter out Jon's activity for Java questions/answers because I don't care.]. Potentially I can let visitors of my site follow SO user's activity and use 'follower' count to find more interesting users for me to follow.

I want to build a knowledge-base that interacts with a case management system.

Support engineers link answers to cases, which would increment the vote for the answer, perhaps also for the question as well.

It would be good to have a way to convert a support case, which would have a "question" field and an "answer" field, into StackExchange question.

It would also be important to have some mechanism for tiered access control, for example, internal only vs. public access. From a business process perspective, it would be best if the conversion from internal to public could be automated, say, after an article received 3 votes.

My need is more in the complete zone than that of the build zone since it's for the StackOverflow Bar.

I've been publicizing the inclusion of alerts on the bar but, I've let the idea go bad to the point of foul smell just because HTML scrapping under Firefox is just... not something you want to self inflict.

In a similar fashion to jjnguy once a Stack Overflow API is available I'd like to help work on an Android application for Stack Overflow. I say help because once the API is available it'll only be a matter of time before such an application is built and it's a great idea to raise awareness for this idea so that the community can build an open-source application for us Android users.

For this, it would be great to take advantage of JSON. Every other answer here has the right ideas as to what an API needs and more personal touches, such as all notification functionality to be working (i.e. like for the reddit is fun app) when you are alerted when you receive a new notification.

I would like to build a Windows Mobile 6/6.5 and a Windows Phone 7 App. It would start off as a way to view rep and search/monitor questions. But as the API extends I would like to see full submits abilities as well.

Features I would like to start...

Keyword/Tag search

User lookup

Rep info (badges/points/avatar)

Track last update (the ability to find/browse updates to questions and answers)

I want a build a plugin for Eclipse and a browser extension for Chrome/Firefox that automatically pulls up related questions from Stack Overflow whenever there is a compile/runtime error. If no matching questions are found, it would allow me to post the question online from the IDE/browser plugin itself.

An ideal API for this task would:

Let me search questions by keywords

Let me do a full-text search for some
compiler/browser error in the
question text.

I want a desktop application (or Windows 7 sidebar gadget) that will pull from all the Stack Exchange sites that I add to it. I want to see answers to my questions, new comments to my questions, hits on my CV, messages on my CV, and comments that other people leave on questions that I comment on or answer.

I'd also like a Windows Mobile app that does some subset of the things above.

I would like a social network based on Stack Overflow. Make it easy to find your friends on Stack Overflow and add them as your fellow Stack Overflowers. Then make a "what's up with your Stack Overflow friends" page and a RSS feed that displays recent activity of questions, answers, comments and voting.

This would enable:

a healthy competition among friends to gain as much rep as they can,

sharing interests of friends ("he is interested in python and he is so cool, so maybe python is worth checking out" ;-)

instead of asking questions directly friend-to-friend, you could post a question on Stack Overflow and all your friends can see what you are asking for and leave a publicly available response for all of the internets to see,

I know Jeff Atwood is against integrating any "social network" features into Stack Overflow, so a separate site is the best solution - it will keep Stack Overflow clean while still providing an alternative for more "socially needy" programmers.

I want to build a site that will show the users only correct and accepted answers, And the user will tag this question in his account and later when needed to face same problem then in place of searching again he will only search in his archived tag. Is it feasible?